FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 1 Marilena Avrigeanu
Progress on Deuteron-Induced Activation Cross Section Evaluation
Marilena Avrigeanu1, Wolfram von Oertzen2, Robin Forrest3, Aura Obreja1, Faustin Roman1, Vlad Avrigeanu1
(1) EURATOM-MEdC Fusion Association, "Horia Hulubei" National Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania(2) Freie Universitat Berlin, Fachbereich Physik, 14195 Berlin, and Hahn-Meitner-Institut, 14109 Berlin, Germany(3) EURATOM-UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB, UK
PN2_IDEI_149/2007 [ http://proiecte.nipne.ro/pn2/ ] [ http://www.cncsis.ro/ ]
FENDL-3 1st Research Co-ordination Meeting NDS/IAEA, Vienna, 2-5 December 2008
http://tandem.nipne.ro/~vavrig/, http://fp6.cordis.lu/fp6/partners/RCN 49105
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 2 Marilena Avrigeanu
IFMIF Data Needs
[U. Fischer, ND2007 & "Nuclear Data Libraries for Advanced Systems: Fusion Devices“,
TM, Nov 2007, IAEA, Vienna]
• Activation/transmutation data
• General purpose neutron data library – Urgent need for qualified IFMIF reference data library– IEAF/EAF (n, p, d), to be further developed, improved and validated– Cross section measurements required for
• neutrons (E >20 MeV): Cr, Co, V, W, Ta, Pb, Bi, Au, Mn• deuterons (E < 40 MeV): Cu, Al, Nb, • protons (E < 12 MeV): Cu, Al, Nb, Ta, W, Au, Pb
– Validation experiments, to be extended/continued
• Reliable gas production cross-section data (H, He)
• Dosimetry data file to be developed for E > 20 MeV (IRDF)
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 3 Marilena Avrigeanu
• Optical Potential - key ingredient of cross-sections calculations
• NO GLOBAL OPTICAL POTENTIAL (OP) for d + Nucleus (A<27) (basis of TW5-TTMI-004-D5)
• COMPARATIVE ANALYSIS of global OMPs for d + 27Al, 63,65Cu, 54,56,58Fe, 93Nb:Lohr-Haeberli (1974): A~40-209, E=8-13 MeVPerey-Perey (1963,1976): A~40-208, E=12-25 MeVDaehnick et al. (1980): A~27-238, E=11.8-90 MeVBojowald et al. (1988): 27Al, 89Y, 120Sn, and 208Pb at Ed=58.7 and 85 MeV
• None of these global OMP describes data at E<15 MeV
• Semi-microscopic OMP by using realistic nucleon-nucleon interaction
• Average of the local OMP parameters for d+27Al,54,56Fe,63,65Cu,93Nb: Phenomenological OMP → cross-sections calculations
• Analysis of deuteron breakup mechanism: Contribution of breakup to the reaction and activation cross sections• Direct Reactions contribution considered through stripping mechanism
• Activation cross sections calculations for d+27Al interaction
INTRODUCTION
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 4 Marilena Avrigeanu
27Al + d : most recent phenomenological potentials
10-1
100
9.8 MeV
10-1
100
9 MeV
0 30 60 90 120 150 180
10-2
10-1
100
101
c.m.
[deg]
58.7 MeV
10-1
100
Daehnick+ (1980) Haixia+ (2006) Han+ (2006)
7 MeV
100
d/
dR
uth
erf
ord
5 MeV
27Al(d,d0)
10-1
100
11 MeV
0 30 60 90 120 150 180
10-1
100
c.m.
[deg]
11.4 MeV
10-1
100
11.8 MeV
10-2
10-1
100
12.8 MeV
10-1
100
d/
dR
uth
erf
ord
13 MeV
10-1
100
15 MeV
10-2
10-1
100
52 MeV
0 30 60 90 120 150 180
100
102
11.8 MeV
d/
d
[m
b/s
r]
0 30 60 90 120 150 180
100
102
104
d/
d
[m
b/s
r]
c.m.
[deg]
15.8 MeV
0 10 20 30 40 50 60100
102
104
c.m.
[deg] d/
d
[m
b/s
r]
63 MeV
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 5 Marilena Avrigeanu
M. Avrigeanu et al., Phys. Rev. C62 (2000) 017001
M. Avrigeanu et al., Nucl. Phys. A693 (2001) 616
M. Avrigeanu et al. Eur. Phys. J. A12 (2001) 399
M. Avrigeanu et al., Int. J. of Mod. Phys. E, 11 (2002) 249
M. Avrigeanu et al., Nucl. Phys. A723 (2003) 104
M. Avrigeanu et al., Nucl. Phys. A 759 (2005) 327
M. Avrigeanu et al, Nucl. Phys. A 764 (2006) 246
M. Avrigeanu et al., Phys. Rev. C62 (2000) 017001
M. Avrigeanu et al., Nucl. Phys. A693 (2001) 616
M. Avrigeanu et al. Eur. Phys. J. A12 (2001) 399
M. Avrigeanu et al., Int. J. of Mod. Phys. E, 11 (2002) 249
M. Avrigeanu et al., Nucl. Phys. A723 (2003) 104
M. Avrigeanu et al., Nucl. Phys. A 759 (2005) 327
M. Avrigeanu et al, Nucl. Phys. A 764 (2006) 246
OPTICAL MODEL : prime tool for all cross section calculations Phenomenological OMP global parameter sets: codes default
Microscopic OPs: reduced uncertainties
SCAT 2000 [O. Bersillon] - pure elastic scattering OP analysis
DFOLD [M. Avrigeanu] - double folding method(nucleons, d, 4,6,8He + 4-124A-target nuclei)
FRESCO - 2.3 [I.J. Thompson]- Coupled Reaction Channel
TALYS - 1.0 [A. Koning, S. Hilaire, M. Duijvestijn] - OMP:ECIS’97; EXCITON; Hauser-Feshbach
STAPRE - H95 (updated) [V.Avrigeanu, M.Avrigeanu] - OMP:SCAT2000; GDH / EXCITON; Hauser-Feshbach
Nuclear Model Calculations
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 6 Marilena Avrigeanu
U(E,R)= dr1 dr2 1(r1) 2(r2) veff(ρ,E,s=R+r1-r2)
1,2 - density distributions of projectile (1) and target (2) veff(,E,r) = F()g(E)v(r)
F() = C[1+e-] (DDM3Y) C[1-] (BDM3Y)
g(E) = 1-0.002E/A (Reid NN interaction)
1-0.003E/A (Paris NN interaction)
v(r) - effective NN-interaction: isoscalar and isovector components of direct and exchange parts of M3Y interaction ( g-matrix using Reid/Paris NN potential )
Microscopic Real Optical Potential
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 7 Marilena Avrigeanu
DME-leading term (Negele-Vautherin'72) (R,R+s)=(R+s/2)Ĵ 1[kF(R+s/2)s] Campi-Bouyssy'78 for average relative momentum, kF=kav kav(r)=5/(3(r))[(r)-(1/4)2(r)]1/2
Kinetic-Energy Density (: MTF-Krivine-Treiner'79) ()=(r)5/3 + ()2/ The frozen-density approximation (Satchler'79, Khoa'94) F()=F[1(r1+s/2)+2(r2-s/2)].
Approximations
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 8 Marilena Avrigeanu
Density distributions & NN-interactions
0 2 4 6 80
20
40
60
80
r [fm]
11 MeV
0
20
40
60
80
9 MeV
0
20
40
60
80 Paris-Negele-Machleidt'01 Paris-Negele-Abbott Reid-Negele-Abbott
7 MeV
0
20
40
60
80 27Al(d,d0)27Al
5 MeV-UD
F(r
) [
Me
V]
0 2 4 6 810-5
10-3
10-1
Negele (1970)
r [fm]
27Al
(r)
[f
m-3 ]
(c)
0.1
0.2
0.3
0.4 2H u
(r)/
r [
fm-3
/2]
Machleidt (CD-Bonn) Machleidt (1989-Paris)
(a)
0 2 4 610-6
10-4
10-2
100
charge density (Abbott) Machleidt-CD-Bonn Machleidt-Paris
2H
(r)
[f
m-3]
(b)
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 9 Marilena Avrigeanu
1
Strzalkowski+ (1962)
9.8 MeV
1
9 MeV
1
Al-Quraishi+ (2000)Schwandt+ (1968)
7 MeV
1
Lohr-Haeberli Daehnick+ This work: microscopic
5 MeV27Al(d,d
0)
(a)
1
11 MeV
0.1
1
/
Ru
the
rfo
rd
11.4 MeV
1Igo+ (1961)
11.8 MeV
1
12.8 MeV
1
Lohr+ (1974)
13 MeV
0 30 60 90 120 150 180
0.1
1
c.m.
(deg)
Joly+ (1963)
15 MeV
1
9.8 MeV
1
9 MeV
0 30 60 90 120 150 1800.01
10
c.m.
(deg)
58.7 MeV(d)
1
7 MeV
1
Haixia+TALYS-1.0This work: phenomenologic
5 MeV 27Al(d,d0)
1
11 MeV
0.1
1
11.4 MeV
1
11.8 MeV
0.1
1
12.8 MeV
1
13 MeV
0.1
1
15 MeV
1
52 MeV
10
20
-W
(M
eV
)
WD local
WD average(b)
WV local
WV average
0 10 20 30 40 50 60
-10
0
10
-U
(M
eV
)
V
D
Ed (MeV)
(c)
0 10 20 30 40 50 600
400
800
1200
R (m
b)
Haixia+ TALYS-1.0 ACSELAM this work
d + 27Al
Ed (MeV)
(e)
Mayo+ (1965)Dubat+ (1974)
1
Strzalkowski+ (1962)
9.8 MeV
1
9 MeV
1
Al-Quraishi+ (2000)Schwandt+ (1968)
7 MeV
1
Lohr-Haeberli Daehnick+ This work: microscopic
5 MeV27Al(d,d
0)
(a)
1
11 MeV
0.1
1
/
Ru
the
rfo
rd
11.4 MeV
1Igo+ (1961)
11.8 MeV
1
12.8 MeV
1
Lohr+ (1974)
13 MeV
0 30 60 90 120 150 180
0.1
1
c.m.
(deg)
Joly+ (1963)
15 MeV
1
9.8 MeV
1
9 MeV
0 30 60 90 120 150 1800.01
10
c.m.
(deg)
58.7 MeV(d)
1
7 MeV
1
Haixia+TALYS-1.0This work: phenomenologic
5 MeV 27Al(d,d0)
1
11 MeV
0.1
1
11.4 MeV
1
11.8 MeV
0.1
1
12.8 MeV
1
13 MeV
0.1
1
15 MeV
1
52 MeV
10
20
-W
(M
eV
)
WD local
WD average(b)
WV local
WV average
0 10 20 30 40 50 60
-10
0
10
-U
(M
eV
)
V
D
Ed (MeV)
(c)
0 10 20 30 40 50 600
400
800
1200
R (m
b)
Haixia+ TALYS-1.0 ACSELAM this work
d + 27Al
Ed (MeV)
(e)
Mayo+ (1965)Dubat+ (1974)
1
Strzalkowski+ (1962)
9.8 MeV
1
9 MeV
1
Al-Quraishi+ (2000)Schwandt+ (1968)
7 MeV
1
Lohr-Haeberli Daehnick+ This work: microscopic
5 MeV27Al(d,d
0)
(a)
1
11 MeV
0.1
1
/
Ru
the
rfo
rd
11.4 MeV
1Igo+ (1961)
11.8 MeV
1
12.8 MeV
1
Lohr+ (1974)
13 MeV
0 30 60 90 120 150 180
0.1
1
c.m.
(deg)
Joly+ (1963)
15 MeV
1
9.8 MeV
1
9 MeV
0 30 60 90 120 150 1800.01
10
c.m.
(deg)
58.7 MeV(d)
1
7 MeV
1
Haixia+TALYS-1.0This work: phenomenologic
5 MeV 27Al(d,d0)
1
11 MeV
0.1
1
11.4 MeV
1
11.8 MeV
0.1
1
12.8 MeV
1
13 MeV
0.1
1
15 MeV
1
52 MeV
10
20
-W
(M
eV
)
WD local
WD average(b)
WV local
WV average
0 10 20 30 40 50 60
-10
0
10
-U
(M
eV
)
V
D
Ed (MeV)
(c)
0 10 20 30 40 50 600
400
800
1200
R (m
b)
Haixia+ TALYS-1.0 ACSELAM this work
d + 27Al
Ed (MeV)
(e)
Mayo+ (1965)Dubat+ (1974)
1
Strzalkowski+ (1962)
9.8 MeV
1
9 MeV
1
Al-Quraishi+ (2000)Schwandt+ (1968)
7 MeV
1
Lohr-Haeberli Daehnick+ This work: microscopic
5 MeV27Al(d,d
0)
(a)
1
11 MeV
0.1
1
/
Ru
the
rfo
rd
11.4 MeV
1Igo+ (1961)
11.8 MeV
1
12.8 MeV
1
Lohr+ (1974)
13 MeV
0 30 60 90 120 150 180
0.1
1
c.m.
(deg)
Joly+ (1963)
15 MeV
1
9.8 MeV
1
9 MeV
0 30 60 90 120 150 1800.01
10
c.m.
(deg)
58.7 MeV(d)
1
7 MeV
1
Haixia+TALYS-1.0This work: phenomenologic
5 MeV 27Al(d,d0)
1
11 MeV
0.1
1
11.4 MeV
1
11.8 MeV
0.1
1
12.8 MeV
1
13 MeV
0.1
1
15 MeV
1
52 MeV
10
20
-W
(M
eV
)
WD local
WD average(b)
WV local
WV average
0 10 20 30 40 50 60
-10
0
10
-U
(M
eV
)
V
D
Ed (MeV)
(c)
0 10 20 30 40 50 600
400
800
1200
R (m
b)
Haixia+ TALYS-1.0 ACSELAM this work
d + 27Al
Ed (MeV)
(e)
Mayo+ (1965)Dubat+ (1974)
DF-real & phenomenological imaginary/s.o. potentials Phenomenological OMP
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 10 Marilena Avrigeanu
d breakup
1 (a) fpTBU= 0.087 – 0.0066 Z + 0.00163 Z A1/3 + 0.0017 A1/3E – 2E-6 ZE2
1 (b) fELBU= 0.031 – 0.0028 Z + 0.00051 Z A1/3 + 0.0005 A1/3E – 1E-6 ZE2
elastic 27Al + d 27Al + n+ p
inelastic (27Al + n) + p (28Al*) + p 27Mg + p + p (2p ch. of 29Si* )
24Na + α + p (pα ch. of 29Si* ) inelastic (27Al + p) + n (28Si*) +n 27Si + n + n (2n ch. of 29Si* )
Empirical breakup enhancement fBU from (d,p) & (d,n) systematics
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 11 Marilena Avrigeanu
Stripping contribution (FRESCO-code; 18 levels of 28Si)
0 30 60 90 120 150
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
Bohne+ (1969)
c.m.
(deg)
d/d
(mb/s
r)
g.s., 0+
27Al(d,n)28Si
Ed=6 MeV
1.779, 2+x102
x104
4.618, 4+
6.276, 3+
x106
x108
7.799, 3+
0 30 60 90 120 150
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
c.m.
(deg)
DR PE+CN DR+PE+CN
7.930, 2+
x103
8.543,6+ + 8.587,3+
x105
9.319, 3+
Bohne+ (1969)
x107
9.379,2+ + 9.41,5+
x109
10.379, 3+
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 12 Marilena Avrigeanu
Stripping contribution (FRESCO-code; 35 levels of 28Al)
0 10 20 30 40 50
1E-11
1E-9
1E-7
1E-5
1E-3
0.1
10
0 30 60 90 120 150
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
1E-6
1E-4
0.01
1
100
Chen+ (1972)
c.m.
(deg)
d/d
(mb/s
r)
g.s., 3+
27Al(d,p)28AlE
d=6 MeV
0.031, 2+
x102
x104
1.014, 3+
2.138, 2+x106
x108
2.272, 4+
x1010
2.656, 4+
3.465, 4-
x1012
x1014
3.591, 3-
4.904, 2-
x1016
5.135, 3-
x1018
0 20 40 60 80 100
1E-28
1E-26
1E-24
1E-22
1E-20
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
1E-6
1E-4
0.01
1
c.m.
(deg)
g.s.
Ed=12 MeV
x103
0.031
x106
1.014
Carola+ (1971)
x109
2.138
x1012
2.272
x1015
2.656
x1018
3.465
x1021
3.591
4.765, 2-
4.904
x1024
x1027
DR PE+CN DR+PE+CN
c.m.
(deg)
g.s. + 0.031
1.014
x104
Maher+(1972)
Ed=23 MeV
x105
2.138x106
2.272
2.656
x107
x109
3.465x1010
3.591
4.033, 5-
x1011
4.315, 1+
x1013
g.s. + 0.031
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 13 Marilena Avrigeanu
Breakup & DR
27Al + d (27Al + n) + p
(T) (B)
(27Al + p) + n
peak centroid: Ex = Ax/Ad*(Einc – 1.44ZdZT/(1.5AT1/3 + Rd) + 1.44ZxZB/(1.5AT
1/3 + Rd)
FWHM: = 0.3 (Einc + 15 MeV ) (1 – AT/1500) [Kalbach, 2007]
0 20 40 600.0
0.2
0.4
0.6
Ed (MeV)
(EB+BFDR) / R
EB+BF /R
DR /R
/
React
ion
d + 27Al(a)
0 5 10 15 20 25 300
5
10
15
Ed (MeV)
Ex
(MeV
) Ep
En
27Al(d,n+p)
(b)
Breakup energies for n & p
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 14 Marilena Avrigeanu
BREAKUP contribution to the SECOND particle emission
σBF(p) vs Ed σBF
(p) vs Ed σBF(n) vs Ed
27Al(n,p)27Mg vs En 27Al(n,α)24Na vs En
27Al(p,n)27Si vs Ep
27Al(n,p)27Mg vs Ed 27Al(n,α)24Na vs Ed
27Al(p,n)27Si vs Ed
[via BF] [via BF] [via BF]
0 5 10 15 20 25 30
0.1
1
10
100
(
mb)
Wilson+ (1976)Bem+ (2007)
27Al(d,2p)27Mg
BF add-on BF add (smooth)
0.002*(p)BF
(a)
(p)BF
27Al(n,p)27
Mg
0 20 40 60
0.01
0.1
1
10
10027Al(d,p)24Na
(p)BF
27
Al(n,)24
Na
BF add-on BF add (smooth)
0.001*(p)BF
(b)
0 5 10 15 20 25 301
10
100
E (MeV)
27Al(d,2n)27Si Wilson+ (1976)
(n)BF
27Al(p,n)27Si BF add-on BF add (smooth)(c)
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 15 Marilena Avrigeanu
d + 27Al: Activation cross-sections
5 10 15 20 250
5
10
15
20
25
(
mb)
Wilson+ (1976)Bem+ (2007) TALYS-1.0 ACSELAM BF+PE+CN BF STAPRE-H
(PE+CN)
27Al(d,2p)27Mg
(c)
0 5 10 15 20 250
100
200
300
400
500
TALYS-1.0 ACSELAM DR+PE+CN FRESCO (DR) STAPRE-H
(PE+CN)
27Al(d,p)28Al (a)
Wilson+(1976)Bem+ (2007)
10 20 30 40 50 600
20
40
60
80
Ed [MeV]
27Al(d,p)24NaMartens+ ('70)Watson+ ('73)Wilson+ ('76)Zarubin+ ('79)Weinreich+('80)Michel+ ('82)Tao Zhen+ ('87)Zhao Wen+ ('95)Takacs+ (2001)Hagiwara+(2004)Nakao+ (2006)Bem+ (2007)
TALYS-1.0ACSELAM
(f)
BF+PE+CN PE+CN BF
10 15 20 250
20
40
60
8027Al(d,2n)27Si
TALYS-1.0 ACSELAM BF+PE+CN BF STAPRE-H
(PE+CN)
(d)
Wilson+ (1976)
0 5 10 15 20 250
200
400
600
800
TALYS-1.0 ACSELAM DR+PE+CN FRESCO (DR) STAPRE-H
(PE+CN)
27Al(d,n)28Si(b)
0 5 10 15 20 250
50
100
150
200
250
TALYS-1.0 ACSELAM STAPRE-H
(PE+CN)
27Al(d,)25Mg Al-Quraishi+(2000): (d,x)
(e)
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 16 Marilena Avrigeanu
Activation cross sections for d + 63,65Cu [ former approach ]
0.1
1
10
100
Fulmer+ (1970)-natCu NPI-Prague (2007)
TALYS EMPIRE
63Cu(d,3n)62Zn[0+ 9.3H]
0
100
200
300
400
[
mb
]
Okamura+ (1971) Gilly+ (1963) NPI-Prague (2007)
TALYS EMPIRE
63Cu(d,p)64Cu [1+ 12.8H]
0
100
200
300
400
Okamura+ (1971) Gilly+ (1963) NPI-Prague (2007)
TALYS EMPIRE
63Cu(d,2n)63Zn[3/2- 38.4M]
0 20 40 600
1
2
3
4
5
6
7
8
9
Ed [MeV]
Baron+ (1963) NPI-Prague (2007)
TALYS EMPIRE
65Cu(d,2p)65Ni[5/2- 2.6H]
0 20 40 600
200
400
600
800
Ed [MeV]
Okamura+ (1971)
Fulmer+ (1970) natCu Gilly+ (1963)
TALYS EMPIRE
65Cu(d,p)66Cu [1+ 5.1M]
0 5 10 15 20 25 300
300
600
900
1200
Ed [Mev]
Okamura+ (1971)
Fulmer+ (1970)) natCu Pement+ (1966) NPI-Prague (2007)
TALYS EMPIRE
65Cu(d,2n)65Zn[5/2- 245D]
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 17 Marilena Avrigeanu
CONCLUSIONS Starting point: available (d,d) and R data for d+27Al,54,56,58,natFe,63,65,natCu,93Nb
poor description by global OMP parameter sets
Semi-microscopic OMP analysisUDF: ρd (charge) & ρAl (charge) & M3Y Paris-NNWD & VSO phenomenological
improved agreement with data adding the dispersion corrections
Phenomenological OMP analysis for 27Al agreement with all available measured data good description of (d,d) data vs. TALYS default OMPs improved description of (d,d) data vs. global OMPs
Completion of d+27Al activation cross sections Deuteron break-up mechanism contribution taken into account DR mechanism considered trough n & p stripping contributions Comparison of STAPRE-H / TALYS-1 activation cross sections
NEED to UPDATE the d-activation libraries
FENDL-3 1st Research Co-ordination Meeting, 2-5 December 2008, IAEA, Vienna 18 Marilena Avrigeanu
Thank you